Tunable Multiwalled Nanotube Resonator

ABSTRACT

A tunable nanoscale resonator has potential applications in precise mass, force, position, and frequency measurement. One embodiment of this device consists of a specially prepared multiwalled carbon nanotube (MWNT) suspended between a metal electrode and a mobile, piezoelectrically controlled contact. By harnessing a unique telescoping ability of MWNTs, one may controllably slide an inner nanotube core from its outer nanotube casing, effectively changing its length and thereby changing the tuning of its resonance frequency. Resonant energy transfer may be used with a nanoresonator to detect molecules at a specific target oscillation frequency, without the use of a chemical label, to provide label-free chemical species detection.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. Non-Provisionalpatent application Ser. No. 11/467,422 filed Aug. 25, 2006, which claimsbenefit of priority to U.S. Provisional Patent Application Ser. No.60/711,937, filed Aug. 25, 2005, both of which are hereby incorporatedby reference in their entirety.

STATEMENT REGARDING FEDERAL FUN DING

This invention was made with U.S. Government support under ContractNumber DE-AC02-05CH11231 between the U.S. Department of Energy and TheRegents of the University of California for the management and operationof the Lawrence Berkeley National Laboratory. The U.S. Government hascertain rights in this invention.

REFERENCE TO A COMPUTER PROGRAM

Not Applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to resonating nanotubes, morespecifically to resonant frequency tunable nanotubes, and still morespecifically to resonant frequency tunable carbon multiwall nanotubes(MWNT).

2. Description of the Relevant Art

Nanoscale resonators, with their low masses, low force-deflectionspring-rate constants, and high resonant frequencies, are capable ofweighing single bacteria [ILIC 00], detecting single spins in magneticresonance systems [RUGA 04], and even probing quantum mechanics inmacroscopic systems [LAHA 04], [BRES 02]. These resonators are typicallycreated from surface-micromachined silicon; however, carbon nanotubesprovide an alternate, nearly ideal building material because of theirlow density, high Young's modulus, and atomically perfect structure.Already there has been much progress in analyzing and constructingnanotube-based resonators [LI 04], [SAZO 04].

Present designs typically either operate at a single frequency or have arelatively narrow frequency range, possibly imposing limitations intheir application.

These resonators are pically micromachined from silicon; however,because of their low density, high Young's modulus, and atomicallyperfect structure, carbon nanotubes provide an alternate, nearly idealbuilding material. Some progress has been made in constructingnartotube-based resonators [SAZO 04]. However, these resonators have anarrow frequency range and obey a relatively complicated physical model.

U.S. Pat. No. 6,709,566, hereby incorporated by reference describes amethod for shaping small three-dimensional articles such as nanotubesexhibiting a layered structure through material removal such that thearticle is controllably shaped to exhibit a desired contour. Typically,material removal does not require use of a chemical etchant and iscarried out while the article and a shaping electrode are positioned incontact material removal relationship with under a potential difference.The invention also relates to nanotubes and small three-dimensionalarticles exhibiting a layered structure having a controllably shapedcontour.

U.S. Pat. No. 6,803,840, hereby incorporated by reference describes atunable nanomechanical oscillator device and system. The nanomechanicaloscillator device comprises at least one nanoresonator, such as asuspended nanotube, designed such that injecting charge density into thetube (e.g. by applying a capacitively-coupled voltage bias) changes theresonant frequency of the nanotube, and where exposing the resonator toan RF bias induces oscillatory movement in the suspended portion of thenanotube, forming a nanoscale resonator, as well as a force sensor whenoperated in an inverse mode. A method of producing an oriented nanoscaleresonator structure with integrated electrodes is also provided in thepatent.

Here is proposed a fundamentally different nanotube resonator, whichtakes advantage of one of carbon nanotubes' most interesting properties.Multiwalled carbon nanotubes (MWNTs), which consist of multiple,concentric nanotubes precisely nested within one another, exhibit astriking telescoping property whereby an inner nanotube core may slidewithin the atomically smooth casing of an outer nanotube shell [CUMI00a]. Already this property has been exploited to build a rotationalnanomotor [FENN 03] and a nanorheostat [CUMI 04]. Future nanomachinessuch as a gigahertz mechanical oscillator are envisioned [ZHEN 02]. Byharnessing this versatile telescoping property in a new fashion, atunable nanoscale resonator has been developed.

BRIEF SUMMARY OF THE INVENTION

This invention provides an apparatus and applications for a tunablemultiwalled nanotube. Such tunable nanotube is embodied here as atunable multiwalled carbon nanotube resonator.

In one embodiment, a tunable resonator may comprising: a) an extendablemultiwalled nanotube having two ends; and b) an extension means attachedto each of the two ends of the extendable multiwalled nanotube; c)whereby the extension means displaces the two ends of the attachedextendable multiwalled nanotube.

The tunable resonator above may further comprise: a) an excitationmeans, which may or may not act in conjunction with the extension means;b) which causes the extendable multiwalled nanotube to vibrate. Oneexample of where the excitation means acts in conjunction with theextension means is where a current is passed first through the extensionmeans, then through the resonator. When the resonator is subjected to amagnetic field, then the impressed current generates an excitation forceon the resonator, causing it to vibrate. Similarly, when the resonatoris subject to an electrostatic field, then an impressed voltagegenerates an excitation force on the resonator, causing it to vibrateThese forces are due to standard electrostatic or electromagnetic forcesgenerally described in first year college physics texts.

The tunable resonator above may have the excitation means comprising: a)an electromagnetic field disposed about the extendable multiwallednanotube; and b) a variable current that passes through the extendablemultiwalled nanotube, no as to cause a vibration in the extendablemultiwalled nanotube.

The tunable resonator extendable multiwalled nanotube may comprise: a) acarbon multiwalled nanotube, comprising at least two walls.Additionally, a deflection sensor means may be provided that detects anamplitude of the extendable multiwalled nanotube deflection.

The extension means may generally be regarded as controlling thedeflection of the resonator, which in conjunction with the excitationmeans, causes the resonator to vibrate. The extension means may beattached to one or both ends of the resonator. If attached to only oneend, then the other end may be fixed, or attached to a differentextension means operating in either the same, or a different manner ofextension. Ultimately, the resonator is either lengthened or shortenedthrough the action of the extension means, thus changing the resonatorfrequency of oscillation.

In another embodiment, a method for tunably resonating a multiwallednanotube may comprise: a) disposing an extendable mount attaching to amultiwalled nanotube at both ends of the multiwalled nanotube; b)displacing the extendable mount to extend the attached multiwallednanotube to a desired displacement; and c) exciting the multiwallednanotube to cause it to vibrate. The method may further comprise: a)detecting an amplitude of the multiwalled nanotube vibration. Again, themultiwalled nanotube may be a carbon multiwalled nanotube.

The methods above may use the exciting step comprised of: a) passing acurrent through the multiwalled nanotube; and b) providing anelectromagnetic field disposed about the multiwalled nanotube.

The methods above may further comprise: a) controlling the desireddisplacement so that the amplitude of the multiwalled nanotube vibrationis maximized at a central resonant frequency; and b) measuring afrequency of the multiwalled nanotube vibration.

In another embodiment, the methods above may further comprise: a)reducing a particle number density of a dissipative fluid disposed aboutthe multiwalled nanotube to increase the Q of the multiwalled nanotube.The fluid may be atomic or molecular, and may be in gaseous or liquidform, or any mixture of the preceding.

In still another embodiment, the methods above may further comprise: a)calculating a change in length of the multiwalled nanotube through achange in the central resonant frequency between a first and secondvalue of the desired displacement.

In another embodiment, a method for measuring force by tunablyresonating a multiwalled nanotube may comprise: a) disposing anextendable mount attaching to a multiwalled nanotube at one end of themultiwalled nanotube; b) detecting an amplitude displacement of themultiwalled nanotube vibration; c) exciting the multiwalled nanotube tocause it to vibrate; d) controlling the desired amplitude displacementso that the amplitude of the multiwalled nanotube vibration is maximizedat a central resonant frequency; and e) measuring a frequency of themultiwalled nanotube vibration. Again, the multiwalled nanotube may be acarbon multiwalled nanotube. Additionally, the exciting step maycomprise: a) passing a current through the multiwalled nanotube; and b)providing an electromagnetic field disposed about the multiwallednanotube.

Alternatively, electrostatic operation may be obtained by placing acharged voltage on the resonator in the presence of an electric field,thereby producing Coulomb forces and thus driving the resonator tooscillate.

In another embodiment, one my add still more steps, comprising: a)applying a force to the extendable mount, resulting in a change inlength of the multiwalled nanotube with a consequent change in centralresonant frequency; b) calculating the magnitude of the force applied tothe extendable mount by the consequent change in central resonantfrequency. In this embodiment, the applying a three step may comprise:a) applying a mass in a gravitational or accelerating field to generatethe force.

In still another embodiment, a label free tunable nanoresonator detectoris made, comprising: a tunable nanoresonator without a chemical label; atuning means, whereby the nanoresonator is tuned to a specific targetoscillation frequency; and a detector means; whereby a specific targetmolecule is detected by the nanoresonator. In this device, the tuningmeans may be any of the above methods of effecting a change in length ofthe tunable nanoresonator. Detection may be made either passively, wheredetection of oscillation of the nanoresonator tuned to a targetdetection frequency is observed, or actively, when driven oscillation ofthe tunable resonator at the target detection frequency results in achange in amplitude of the oscillations, indicating the presence of thetarget molecule vibration. In this device a specific chemical labelsensor is not required, as the molecular vibration is directly detectedwithout any bonding of the molecule to the tunable nanoresonator.

In another embodiment, a method of label free tunable nanoresonatordetection is disclosed, comprising: providing a tunable nanoresonatorwithout a chemical label; tuning the nanoresonator to a specific targetoscillation frequency; and means for detecting a specific targetmolecule by a resonant energy transfer with the nanoresonator. Thesedetails, and the means for detecting, are described above.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The invention will be more fully understood by reference to thefollowing drawings, which are for illustrative purposes only:

FIG. 1A is a schematic of a tunable nanoresonator. A specially preparedMWNT is suspended between a metal electrode and a mobilepiezoelectrically controlled contact. Varying the length of the nanotubebeam through the controlled telescoping of the inner nanotube core fromthe outer nanotube shell tunes its resonant frequency. Operating thedevice in an external magnetic field, {right arrow over (B)}, allowsactuation with alternating current passing through the nanotube via theLorentz force.

FIG. 1B is a drawn representation of a photomicrograph (in thisinstance, from a transmission electron microscope) of a tunablenanoresonator device in action. The top two images show thenanoresonator at one extension before resonance (sharp) and duringresonance (blurred). The bottom two images show the nanoresonator afterthe extension of the MWNT to a longer length, and corresponding to alower fundamental resonant frequency.

FIG. 1C shows composite image of line profiles of a nanotube during afrequency sweep through resonance, Bright and dark horizontal streaks,useful for resonance detection, result from under-focusing the TEMimage. A Lorentzian fit to the maximum (white) regions of the imagedetermines the resonant frequency, amplitude, and quality factor.

FIG. 2A is a graph plotting frequency (in MHz) versus extension (in nm),which demonstrates the tuning process. The data follow the

$\frac{1}{L^{2}}$

dependence expected from the Euler-Bernoulli resonance equation.

FIG. 2B is a graph of a typical resonance peak with amplitude (inarbitrary units) versus frequency (in MHz).

FIG. 3A is a drawn representation of a prior art electron micrograph ofa single end mounted carbon nanotube of a fixed length vibrating at itsfundamental frequency of 315 kHz.

FIG. 3B is a drawn representation of a prior art electron micrograph ofa single end mounted carbon nanotube of a fixed length vibrating at itsfirst harmonic frequency of 1.80 MHz.

FIG. 4A shows typical tuning curves for four nanoresonator devices. Atheoretical model provides a good fit to the data and yields reasonablevalues for the Young's modulus of each device. The inset shows anincrease in dissipation (following a rough 1/Q curve) with beamextension for one device.

FIG. 4B shows typical 1/Q) data points for the four nanoresonatordevices of FIG. 4A at various lengths.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Definitions

Nanotube as used herein refers to a solid, cylindrically shaped, anddiscrete fibril typically characterized by a substantially constantdiameter of typically about 1 nm to about 100 nm, preferably about 2 nmto about 50 nm. in addition, the nanotube typically exhibits a lengthgreater than about 10 times the diameter, preferably greater than about100 times the diameter.

Multiwalled nanotube (MWNT) refers to nanotubes having a layeredstructure, such as a fullerene-like structure, so that the nanotubecomprises an outer region of multiple continuous layers of ordered atomsand an optional distinct inner core region or lumen. The layers aredisposed substantially concentrically about the cylindrical axis of thefibril. One example of a MWNT is a carbon MWNT.

Resonator as used herein refers to an extendable MWNT that is use as avibrating mechanical oscillator.

Introduction

FIG. 1A is a schematic drawing of a tunable nanoresonator 100. A MWNT110 is suspended between a metal electrode 120 and a mobile,piezoelectrically controlled contact 130. By peeling the outer shell ofthe MWNT [COMI 00b] and exposing the inner core of the MWNT, one mayharness its unique telescoping ability. Like a trombone player shiftingnotes, one may controllably slide the inner nanotube 140 from its casing150 using the mobile contact, effectively changing the length of theMWNT and thereby tuning its resonant frequency. In the top image 160 ofFIG. 1A, the resonator is fully retracted and has a relatively highresonant frequency. In the bottom image 170 of FIG. 1A, the resonator isextended and consequently has a lower resonant frequency. By operatingthe device in an external magnetic field 180 and applying alternatingcurrent 190, one may excite the mechanical vibrations of the nanotubevia the Lorentz force [CLE. 96]. With a transmission electron microscope(TEM) it is possible to detect these vibrations through the physicaldisplacement of the beam.

As described previously, the resonator may be operated by Coulomb forcesin an electrostatic field (not shown in the Figures).

Sketched outlines obtained from transmission electron micrographs inFIG. 1B show a tunable nanoresonator in action. The first two images 210and 220 show the nanotube beam at one extension before resonance (sharp)210 and during resonance 220 at 225 MHz (blurred). The final two images230 and 240 show the nanotube beam after the inner nanotube has beentelescoped out 50 nm 230 (prior to resonance. The resonance frequencyhas shifted downward to 193 MHz 240.

Resonance peaks are detected by analyzing video from the TEM with animage processing routine. For each video frame in a rectangular regionsuch as 250, an image such as the one sketched in FIG. 1B is averagedalong the length of the nanotube to provide a single time-slicerepresenting the state of the nanotube. These slices, when combined,form a composite image 300, FIG. 1C, showing the amplitude of resonanceas a function of time, or because frequency is ramped linearly, as afunction of frequency. A Lorentzian fit 305 to the maximum (white)values 310 and 320 of the image gives values for the resonant frequencyand quality factor, Q. FIG. 1C shows a typical resonance-response of anexperimental nanoresonator.

Analysis of a Nanoresonator

The resonance frequency of the tunable nanoresonator obeys theEuler-Bernoulli beam equation, which makes explicit the dependence ofthe resonance frequency on the total length of the tube. The nanotubebeam is treated as a continuum, elastic medium subject to thedifferential equation:

${{\frac{\partial^{2}}{\partial x^{2}}\left( {E\; I\frac{\partial^{2}y}{\partial x^{2}}} \right)} - {\frac{\partial}{\partial x}\left( {T\frac{\partial y}{\partial x}} \right)}} = {{- \rho}\; A\frac{\partial^{2}y}{\partial t^{2}}}$

where y(x) is the transverse displacement of the beam along its length,x is the position along the length of the beam, E is the Young'smodulus, I is the areal moment of inertia, T is the tension, ρ is thedensity, t is time, and A is the cross-sectional area [SOUT 69]. For acylindrical beam with outer and inner radii, r_(outer) and r_(inner),I=π(r_(outer) ⁴−r_(inner) ⁴)/4. Though strictly speaking, the MWNTdevice is not a simple cylindrical beam, but rather a combination of twocylindrical beams, the outer shell nanotube and the inner core nanotube,and moreover its geometry changes during operation.

To simplify' analysis of the nanoresonator, however, it is modeled assimple cylindrical beam with effective values of E, I, ρ, T, l, A,r_(outer), and r_(inner) which remain constant over the length of thebeam and during operation. Applying the boundary conditions of adoubly-ciamped system with beam length, l, (y(0)=0, y′(0)=4, y(l)=0,y′(l)=0) and solving the equation for the resonant frequency at thefundamental mode gives [SOUT 69]:

${f_{0} \approx {\frac{22.4}{2\pi \; l^{2}}\frac{\sqrt{{EI} + {0.024\mspace{11mu} {Tl}^{2}}}}{\rho \; A}}},$

where r_(outer) is the effective radius of the outer wall of thenanotube system, r_(inner) is the effective radius of the inner core ofthe nanotube system, E is the Young's modulus, and ρ is the density.Effective radii are used to account for the fact that the actual radiiare not constant across the length of the nanotube and change duringtelescoping. Numerical solutions for the fundamental mode frequencyformula above using more complex two-cylinder and MWNT bundle modelsindicate that this approximate solution is accurate to within fivepercent for typical devices over their entire range of operation

Tension in this device is supplied by the van der Waals attractionbetween the core nanotube and its shell, F_(vdW)=(0.2 J/m²)·C where C isthe core nanotube's circumference [CUMI 00a]. Interestingly, as aresult, tension remains constant regardless of extension, temperature,or other environmental factors, allowing robust and reproducibleresults.

At the cost of increased complexity, the precise operation of thevibrating MWNT may be modeled, taking into account the stiffness of themounting locations, the varying dimensions of the plurality of walls,and their disposition of length. For even more complexity, the nonlineareffects of high amplitude vibrations may be modeled, although such amodel may no longer use a simple constant EI in the model, and insteaduse an EI(x,y) that is a function of spatial coordinates (x,y).

Experimental Results

As a demonstration of the ability to tune the resonator, in FIG. 2Aappears a plot 300 of the resonance frequency versus extension lengthfor a typical nanoresonator, The resonance frequency follows a predicted

$\frac{1}{L^{2}}$

dependence. Moreover, from a curve fit 310 may be used to calculate theYoung's modulus of a MWNT to be approximately 1.2 T Pa, which appears tobe in agreement with accepted values [PONC 99]. Also apparent in thegraph is the extreme sensitivity of the resonance frequency to theextension length; 100 nm corresponds to a 5 MHz shift. Some othertunable resonator devices have shown sensitivities as great as 1 nm per1 MHz shift. The extreme sensitivity of resonance frequency to thelength of the beam suggests possible application as a nanoscalepositioning device or an extremely sensitive strain gauge.

FIG. 2B shows a typical resonance peak that was observed by sweepingfrequencies while maintaining the same extension 320. Current detectiontechniques require that the resonator be driven at large amplitudes,likely in the non-linear oscillation regime. This could explain therelatively low quality factor (Q=244) and the odd shape of the resonancepeak. Magnetomotive detection [CLEL 96] should allow for smalleramplitudes, which may increase the quality factor. Note that non-linearoscillation is when small angle approximations such as sin(θ)≈θ nolonger remains approximately correct.

FIG. 3A is a drawn representation of a prior art electron micrograph ofa single end mounted 410 carbon nanotube fixed at one end 420 vibratingat its fundamental frequency of 315 kHz. The other end 430 is free tovibrate. This resonator is oscillating at its fundamental, lowest mode440.

FIG. 3B is a drawn representation of a prior art electron micrograph ofa single end mounted carbon nanotube identical to that of FIG. 3A of thesame fixed length vibrating at its first harmonic frequency of 1.80 MHz.Here, the fixed end 440 is mechanically rigid compared to the nanotube,and the other end 450 is free to vibrate. The harmonic resonanceenvelope 460 shows that there is one point of zero amplitude 470 downthe length of the nanotube besides the fixed end 440.

To demonstrate an ability to tune the nanoresonator, a plot of resonantfrequency versus beam extension for four devices is shown in FIG. 4A. Asexpected, extended nanotubes produce lower frequencies as shown by allof the platted lines. Also, each device covers a relatively wide rangeof frequencies, and together the devices span nearly the entire spectrumfrom 30 MHz to 300 MHz, Apparent in the graph is the extreme sensitivityof resonant frequency to beam extension, more than 1 MHz/nm for onedevice, suggesting possible application as a precision distance sensoror strain gauge.

In FIG. 4B, one finds a plot of inverse quality factors versus beamlength in nm. One sees that these inverse quality factors are generallyless than 0.01, implying a Q of greater than 100—a fairly high qualityfactor for a mechanical resonator.

The measured maximum transverse displacement of these devices as afunction of position is consistent with that of a doubly-clamped beamvibrating in its fundamental mode. Using the equation above to calculatef₀, one may fit curves to the experimental tuning data in FIG. 4A, Onlythe Young's modulus and an offset to the length of the beam were used asfitting parameters. Due to current fabrication technique limitations,some of the manufactured tunable nanoresonators are composed of nanotubebundles rather than individual nanotubes resulting in lower values forthe effective Young's modulus, which may vary from one device toan-other. Also, the exact location of the sample-side clamp is oftenobscured in transmission electron microscope (TEM) imaging requiring theusage of a length offset. Specifically, here the change in length of thebeam and determine the total length through the fitting parameter isdirectly measured. The plots in FIG. 4A show frequency versus the entirefitted length. The data follow the curves well and give reasonablevalues for the Young's modulus of a MWNT (1.3 TPa) [PONC 99] or MWNTbundles (20 GPa, 24 GPa, and 59 GPa)[DALT 03],

Nanoresonator Dissipation

As well as having many practical applications, the tunable resonatoralso provides an excellent platform Cor studying the physics ofdissipation. FIG. 4B is a plot of energy dissipation (Q⁻¹) as a functionof extension for one device. Note that both Q and (2⁻¹ are pure numbers,with no units associated with them. There appears to be a significant(p-value=0.03) positive correlation between dissipation and extension.

Possible dissipation mechanisms include eddy current damping, clampingloss, thermoelastic effects, core-shell sliding friction, and variousirreversible processes involving surface defects and adsorbents. Eddycurrent damping [CLET 99], though it would exhibit a positivecorrelation with extension, cannot account for the magnitude of theincrease in dissipation, Clamping loss and thermoelastic dissipationboth have a frequency dependence that would cause dissipation todecrease as length increases, opposite to what is observed. [BRAG 85]Moreover, thermoelastic dissipation is likely greatly suppressed becausethe nanotube may telescope to increase its length rather than stretch.Sliding friction could depend on overlap length between the corenanotube and shell nanotube; however again, dissipation would likelydecrease with increased extension because there would be less overlap.[PERS 00] Surface losses therefore remain the most likely candidate forthe dominant form of dissipation here. This important size-dependentcontributor to dissipation has been suspected in other nanoscaleoscillators [YAKU 00].

Surface losses are typically modeled through the addition of a thindissipative layer to the resonator's surface. Though our experimentswere conducted in high vacuum (10⁻⁷ Torr), the surface of the nanotube,even the newly exposed portion following telescoping, is likely coveredwith more than a monolayer of adsorbents, which functions as thedissipative layer. Dissipation, defined as the inverse of the qualityfactor, is given by: Q⁻¹=ΔW/W₀, where ΔW is the energy lost per cycleand W₀ is the energy originally stored in the resonator. Stored energyis related to total resonator volume while energy lost per cycle isrelated to the volume of the dissipative surface layer, resulting indissipation proportional to the surface- to-volume ratio. Thus, in mostnanoscale resonators, dissipation is inversely proportional to length.[MOHA 02] Curiously, in the nanoresonator tested here, the actual volumeof the resonator remains constant during extension giving a dissipationthat is directly proportional to length, Q⁻¹αS/VαL.

The unique high-Q tunable nanoresonator shown here exhibits promise as aprecise mass, force, position, or frequency sensor. It has demonstrateda wider frequency range than competing tunable nartoresonator designs.Also, its unique sliding ability lends itself to position sensingapplications unlike other immobile resonators. Finally, its nearlyperfect atomic structure and precisely controlled geometry make it anideal tool to study the physics of dissipation.

By harnessing the almost frictionless sliding in telescoping MWNTs, afundamentally new breed of tunable nanoscale resonator has been created.This resonator is unique in that it is the only known nanoresonatortunable via an effective length change, which suggests various nanoscalepositioning or strain measurement applications. Also because thefrequency follows a

$\frac{1}{L^{2}}$

dependence, this resonator has a relatively wide frequency rangecompared to other tunable resonators. These advantages make this tunablenanoresonator an interesting candidate for further study and directedapplications. In particular, the ability to tune to specific oscillationfrequencies allows tunable nanoresonator to readily transfer resonanceenergy from specific vibrational modes of certain target molecules, asfurther described below.

Resonant Energy Transfer and Label-Free Chemical Detection

By operating a nanoresonator at a constant, specific, frequency it ispossible to detect resonant energy transfer between the nanoresonatorand a target molecule. The chemical bonds within a given molecule giverise to high frequency oscillations between the atomic constituents inthe molecule. Further, specific chemical groups of atoms have their ownchemical resonant frequencies. Thus, for a particular chemical group, orfor a specific molecule, it may be possible to choose a specificoscillatory target frequency that is unique to the target molecule.Then, detection of resonant energy transfer between a properly tunednanoresonator and the target molecule, it is possible to detect thepresence of the target molecule. Such detection would be practicedwithout the need for specific chemical labels, and hence would belabel-free.

There are two broad methods thought for achieving such resonant energytransfer detection. A first method would be to have a nanoresonatortuned to the particular target frequency, and then to detect the onsetof oscillations in the nanoresonator. Such onset would be indicative ofchemical bonds vibrating at the target frequency, and would therebyindicate the presence of the target molecule. Second, the nanoresonatorcould be oscillated at the target frequency, and diminution of theamplitude of oscillation would indicate the presence of the targetmolecule.

Similarly, the two methods above could be used to detect certain targetchemical groups common to many molecules by resonant energy transfer ofvibrations at resonant frequencies common to the target chemical group.

Ideally, both the fundamental mode of the nanoresonator and thefundamental mode of the target oscillation would be the same, therebynot introducing any aliasing issues with modal overlap. Certainly, inthe simplest implementation, both fundamental frequencies would be thesame.

yet another embodiment, the nanoresonator could be frequency swept, soas to detect multiple peaks of chemical vibrational modes, much as aswept frequency generator could be used to detect resonances andtransfer functions in analog electrical circuits.

in any of the embodiments above, it would appear that there is nolinking chemical bond required to detect target molecules. Thus, “labelfree” detection would be possible. This means that a single detectionsystem may be used to detect many different molecules without the needfor a new chemical functionalization (or labeling) of the detector.Since the detector is “label free”, in theory continuous measurementsmay be made without cleaning, resetting, or degrading the sensor.

Such a type of detector system would appear to be one of the mostimportant challenges to sensing. Since the detector system describedhere could detect virtually anything, it can be directly compared withother detection devices that have been modified to detect only a singlemolecular species. The results possible here would be obtainable muchmore efficiently because only one detector would be all that would beneeded for all species, as opposed to a new detector for each and everyspecies.

REFEREENCES

The following reference are referred to in the text of the specificationabove with brackets [xxxx nnL] referring to reference “xxxx nnL”.

-   [BRAG 85] Braginski D, V B., et al., Systems with small dissipation,    1985, Chicago: University of Chicago Press. xii, 145.-   [BRES 02] Bressi, G., et al., Measurement of the Casimir force    between parallel metallic surfaces. Physical Review Letters, 2002.    88(4).-   [CLEL 96] Cleland, A. N. and M. L. Roulces, Fabrication of high    frequency nanometer scale mechanical resonators from bulk Si    crystals. Applied Physics Letters, 1996. 69(18): p. 2653-2655.-   [CLEL 99] Cleland, A. N. and M. L. Roukes, External control of    dissipation in a nanometer-scale radiofrequency mechanical    resonator, Sensors and Actuators a-Physical, 1999. 72: p. 256-261.-   [CRAI 00] Craighead, H. G., Nanoelectromechanical systems,    Science, 2000. 290(5496): p. 1532-1535.-   [CUMI 00a] Cumings, J. and A. Zettl, Low-friction nanoscale linear    bearing realized multiwall carbon nanotubes. Science, 2000.    289(5479): p. 602-604.-   [CUMI 00b] Cumings, J., P. G. Collins, and A. Zettl,    Materials—Peeling and sharpening multiwall nanotubes. Nature, 2000.    406(6796): p. 586-586.-   [CUM104] Curnings, J. and A. Zettl, Localization and nonlinear    resistance in telescopically extended nanotubes. Physical Review    Letters, 2004. 93(8).-   [DALT 03] Dalton, A. B., et al., Super-tough carbon-nanotube    fibres—These extraordinary composite fibres can be woven into    electronic textiles. Nature, 2003. 423(6941): p. 703-703.-   [FENN 03] Fennimore, A. M., et al., Rotational actuators based on    carbon nanotubes. Nature, 2003. 424(6947): p, 408-410,-   [RAC 00] IIic, B., et al., Mechanical resonant immunospecific    biological detector. Applied Physics Letters, 2000. 77(3): p.    450-452.-   [LAHA 04] LaHaye, M. D., et al., Approaching the quantum limit a    nanomechanical resonator, Science, 2004. 304(5667): p. 74-77.-   [LI 04] Li, C. and T.-W, Chou, Mass detection using carbon    nanotube-based nanomechanical resonators. Applied Physics    Letters, 2004. 84(25): p. 5246-5248.-   [MOHA 02] Mohanty, P., et al., Intrinsic dissipation in    high-frequently micromechanical resonators. Physical Review B, 2002.    66(8).-   [PERS 00] Persson, B. N. J., Sliding friction: physical principles    and applications. 2nd ed. Nanoscience and technology, 2000, Berlin;    New York: Springer. xi, 515.-   [PONC 99] Poncharal, P., et al., Electrostatic deflections and    electromechanical resonances of carbon nanotubes. Science, 1999.    283(5407): p. 1513-1516.-   [RUGA 04] Rugar, D., et al., Single spin detection by magnetic    resonance force microscopy. Nature, 2004. 430(6997): p. 329-332.-   [SAZO 04] Sazonova, V., et al., A tunable carbon nanotube    electromechanical oscillator. Nature, 2004. 431(7006): p, 284-287,-   [SOUT 69] Southwell, R. V., An introduction to the theory of    elasticity for engineers and physicists, 1969, New York,: Dover    Publications. vi, 509 p.-   [YASU 00] Yasumura, K. Y., et al., Quality factors in micron-and    submicron-thick cantilevers. Journal of Microelectromechanical    Systems, 2000. 9(1): p. 117-125.-   [ZHEN 02] Zheng, Q. S. and Q. Jiang, Multiwalled carbon nanotubes as    gigahertz oscillators. Physical Review Letters, 2002. 88(4).

CONCLUSION

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication or patent application were eachspecifically and individually indicated to be incorporated by reference.

The description given here, and best modes of operation of theinvention, are not intended to limit the scope of the invention. Manymodifications, alternative constructions, and equivalents may beemployed without departing the scope and spirit of the invention.

1. A method for measuring force by tunably resonating a multiwallednanotube, comprising: a) disposing an extendable mount attaching to amultiwalled nanotube at both ends of the multiwalled nanotube; b)detecting an amplitude of the multiwalled nanotube vibration; c)exciting the multiwalled nanotube to cause it to vibrate; d) controllingthe desired displacement so that the amplitude of the multiwallednanotube vibration is maximized at a central resonant frequency; and e)measuring a frequency of the multiwalled nanotube vibration.
 2. Themethod of claim 1 wherein said multiwalled nanotube is a carbonmultiwalled nanotube.
 3. The method of claim 1, wherein the excitingstep comprises: a) passing a current through the multiwalled nanotube;and b) providing an electromagnetic field disposed about the multiwallednanotube.
 4. The method of claim 1, further comprising: a) applying aforce to the extendable mount, resulting in a change in length of themultiwalled nanotube with a consequent change in central resonantfrequency; b) calculating the magnitude of the force applied to theextendable mount by the consequent change in central resonant frequency.5. The method of claim 4, wherein the applying a force comprises: a)applying a mass in a gravitational field to generate the force.
 6. Alabel free tunable nanoresonator detector, comprising: a) a tunablenanoresonator without a chemical label; b) a tuning means, whereby thenanoresonator is tuned to a specific target oscillation frequency; and adetector means; d) whereby a specific target molecule is detected by thenanoresonator.
 7. A method of label free tunable nanoresonatordetection, comprising: a) providing a tunable nanoresonator without achemical label; b) tuning the nanoresonator to a specific targetoscillation frequency; and c) means for detecting a specific targetmolecule by a resonant energy transfer with the nanoresonator.